(This is a direct consequence of the tight frame's reconstruction formula and the fact that a UNTF has unit-norm frame elements; furthermore, since the columns have unit norm, it is not difficult to see that the rows will necessarily have norm \(\sqrt{N/M}\) .)
In addition to being able to test that an ensemble is a UNTF, various UNTFs can be constructed using spectral tetris [1]} (though such frames necessarily have \(N\ge 2M\) ), and every UNTF can be constructed using the recent theory of eigensteps [2]}, [3]}.
Now that UNTFs have been properly introduced, we relate them to almost injectivity for phase retrieval:
